The speaker tells us what the secret is herself:

I will tell the secret to you,
to you, only to you.
Come closer. This song

is a cry for help: Help me!
Only you, only you can,
you are unique

at last.

That her song is not an alluring and seductive call, but actually a cry for help and escape, is the siren's secret.  She is crying for help because she hates her job.  She says in the large stanza that she doesn't enjoy the island (her home) or the "two feathery maniacs" (her peers).  She doesn't enjoy singing the song, either. 

What is revealed immediately after she reveals the secret, however, is that pretending to reveal it is just a ploy on the part of the siren:

Alas
it is a boring song
but it works every time.

She has lured the audience to his death.  Although the song is "boring", it does "work."  It appears to matter not that she hates her job.  She continues with it, perhaps because she has no other choice.